9 research outputs found
The operator approach to dynamic Strong Stackelberg Equilibria
The ISDG12-GTM2019 International Meeting on Game Theory: joint meeting of “12th International ISDG Workshop” and “13th International Conference on Game Theory and Management”International audienc
On the Value Iteration method for dynamic Strong Stackelberg Equilibria
International audienc
Minimum Violation Control Synthesis on Cyber-Physical Systems under Attacks
Cyber-physical systems are conducting increasingly complex tasks, which are
often modeled using formal languages such as temporal logic. The system's
ability to perform the required tasks can be curtailed by malicious adversaries
that mount intelligent attacks. At present, however, synthesis in the presence
of such attacks has received limited research attention. In particular, the
problem of synthesizing a controller when the required specifications cannot be
satisfied completely due to adversarial attacks has not been studied. In this
paper, we focus on the minimum violation control synthesis problem under linear
temporal logic constraints of a stochastic finite state discrete-time system
with the presence of an adversary. A minimum violation control strategy is one
that satisfies the most important tasks defined by the user while violating the
less important ones. We model the interaction between the controller and
adversary using a concurrent Stackelberg game and present a nonlinear
programming problem to formulate and solve for the optimal control policy. To
reduce the computation effort, we develop a heuristic algorithm that solves the
problem efficiently and demonstrate our proposed approach using a numerical
case study
Computing Stackelberg Equilibria in Discounted Stochastic Games
Stackelberg games increasingly influence security policies deployed in real-world settings. Much of the work to date focuses on devising a fixed randomized strategy for the defender, accounting for an attacker who optimally responds to it. In practice, defense policies are often subject to constraints and vary over time, allowing an attacker to infer characteristics of future policies based on current observations. A defender must therefore account for an attacker's observation capabilities in devising a security policy. We show that this general modeling framework can be captured using stochastic Stackelberg games (SSGs), where a defender commits to a dynamic policy to which the attacker devises an optimal dynamic response. We then offer the following contributions. 1) We show that Markov stationary policies suffice in SSGs, 2) present a finite-time mixed-integer non-linear program for computing a Stackelberg equilibrium in SSGs, and 3) present a mixed-integer linear program to approximate it. 4) We illustrate our algorithms on a simple SSG representing an adversarial patrolling scenario, where we study the impact of attacker patience and risk aversion on optimal defense policies